THE MEASURED PERFORMANCE OF A PLANEWAVE GENERATOR PROTOTYPE
Clifton C. Courtney and Donald E. Voss.
Voss Scientific, 418 Washington St., SE
Albuquerque, NM 87108
Randy Haupt
Utah State University, 4120 Old Main Hill
Logan, UT 84322-4120
Larry LeDuc
412 TW / EWD, 30 Hoglan Ave.
Edwards Air Force Base, CA 93524-8210
ABSTRACT
The fundamental concepts of operation of a Planewave
Generator1 (PWG) were described in an earlier paper. In
the present paper the measured performance of a proof of
performance experiment are reported. First, we will
briefly describe the concepts and architecture of the
experimental configuration. Next, measurements of the
electromagnetic field created by the PWG prototype in a
specified test zone will be presented. A planewave figure
of merit (FOM) has been defined earlier, and the
measured FOM of the PWG will be compared with the
FOMs of the field of a single antenna, and of a uniformly
illuminated transmit array.
We first discuss the
experimental strategy, and our use of superposition to
minimize the hardware required for the demonstration.
We then present measured data that shows that a
minimally configured PWG can produce field
distributions that are planewave-like over a limited spatial
extent, and that its field demonstrates planewave qualities
that significantly exceed those achievable by a typical
transmit antenna, or uniformly-illuminated array. We also
present data that relates the size and quality of the
planewave-like field in a test zone in terms of the number
of elements in the PWG transmitting array. Finally, we
present a scaling relation for the PWG, and show that the
radiated field produced by the experimental hardware
agrees well with the field predicted by simulation.
Keywords: planewave generator, far field, near field,
antenna, experimental measurement, T-factor
1. INTRODUCTION
The Voss Scientific Planewave Generator (PWG) concept
relies on a number of transmitters operating in unison to
create a desired, planewave-like field distribution over a
specified and spatially limited region of space. The phase
1
Patent Pending
and amplitude of the microwave signals (nominally 3 GHz
for these experiments) that drive each transmit antenna of
the PWG are independently controlled by a computer and
microwave control circuits as described in [1]. The
purpose of the Proof of Principle (PoP) experiment
described in this paper was to demonstrate the PWG
concept and its potential capability, and to develop scaling
laws that determine the PWG size (number of transmit
channels) and configuration (physical layout) required to
realize a user-specified performance criterion.
To conduct the PoP with a minimal hardware investment
we have designed an experiment to demonstrate PWG
operation by utilizing the superposition principle of
electromagnetics. Below, we describe the basic concepts
of the experiment, the experimental hardware design, and
data collection and reduction schemes. We then present
measured data of the performance of the PWG, and
compare experimental results with simulations of the
PWG. Finally, we include analysis that indicates the
scaling properties of the PWG. To begin, we present the
experimental objectives.
2. EXPERIMENTAL OBJECTIVES
The three objectives for the PoP experiment and PWG
demonstration were to:
• show that a minimally configured PWG system (small
number of radiators) can produce useful field
distributions. This means that the field distributions
are planewave-like over limited (but useful) spatial
extents, and demonstrate planewave qualities that
significantly exceed those achievable by a standard
antenna, or a uniformly-illuminated array.
• show that the size and quality of the planewave-like
field in a test zone is scalable with the size and
number of transmitting elements in the PWG
transmitting array; and
• show that the radiated field produced by the PoP
experimental hardware matches the field predicted by
analysis and simulation(s).
3. EXPERIMENTAL CONFIGURATION
3.1 Experiment Concept – The PWG normally utilizes a
number of transmitters, each with independent amplitude
and phase control, to create a desired field distribution
over a user-specified region of space. For the PoP
experiment we have implemented a hardware design that
is inexpensive (to the extent any microwave hardware is
inexpensive) and easy to assemble and operate. The
concept for the experiment is shown in Figure 1. In the
figure a single transmit antenna and single
electromagnetic field sensor are indicated. The transmit
antenna is located at one possible position, and the
weighted sum of the fields produced by the transmit
antenna operating at each transmit position in the linear
array constitutes the field of the virtual PWG indicated in
the figure.
The virtual PWG operates as follows. A transmit antenna
is first driven by a microwave generator at a constant
power level and phase. A receive probe is positioned at
some distance in front of the transmitter locations, and as
the transmit antenna radiates, measurements of the probe’s
output signal (proportional to the electromagnetic field)
are made at many positions along the extent of the
distance traveled by the probe.
After the first
measurement is completed, the transmit antenna is
repositioned to another physical site corresponding to the
y
location of a different transmit antenna in the PWG.
Again, measurements of the radiated field are made at the
same locations where the field was measured previously.
This process is repeated until the field has been measured
for all locations of the transmit antennas. We then utilize
the principle of superposition [2] to synthesize the
radiated field due to the simultaneous transmission of all
PWG transmitters.
Combining the individual field
measurements with complex weighted values determined
by the PWG simulations mimics PWG performance. This
technique allows the demonstration of the capability of an
actual PWG (one with many transmitters, and a capacity
to drive each with independent and coherent signals)
without the necessity of multiple transmitters. We
recognize that certain aspects of the actual configuration
are not created in this test, most notably transmitter
mutual coupling.
3.2 PWG Test Bed Hardware Description - A custommade test bed hosts the TX and RX antennas, and a
computer-controlled linear positioner.
Its rigid
construction of extruded aluminum unistrut permits
precise and repeatable physical configuration of the PWG.
The test bed, depicted in the illustration of Figure 2, was
designed to allow adjustments in its physical
configuration such as separation between the transmit
position and receive position, heights of the transmit and
receive antennas, and separation between the transmit
S en so r trav els th ro ug h p la ne w av e reg ion
L in ear Track P o sitio ne r
T o tal field is th e
S U P E R P O S IT IO N o f th e field
fro m each tran sm it an ten n a
E M S en sor : R e ceiv e
D e sired P la ne w a ve R e gio n
z = z0
R ad iated field o f tran sm it
an ten n a w h en tran sm it an ten n a
is at th is lo catio n
R ad iated fie ld of
tran sm it a nten na
z = 0
Tran sm it
A n te nn a
(A 0 , M0 )
M icro w ave
S o u rce
(A 0 , M0 )
Tra ns m it statio n
sep aratio n
(A 0 , M0 )
(A 0 , M0 )
(A 0 , M0 )
V IR TU A L P L A N E W A V E G E N E R A T O R
Figure 1 - Schematic diagram of the Proof of Principle hardware simulation of the Plane Wave Generator
Once the measurements of the radiated field had been
made for multiple positions of the transmit antenna, the
field from an actual PWG was determined using
superposition. The test zone field was synthesized from
the field measurements made on the PWG test bed in two
ways. The synthesized fields were formed as follows.
antenna locations.
Dielectric
Antenna Post
Receive antenna
Motorized Linear
Positioner
Transmit
antenna
Al unistrut
Testbed
Support
Frame
Figure 2. PWG Test Bed.
As indicated in the figure the transmit antenna is located
on one side of the test bed, and manually positioned to the
desired location. Fiducial markings on the base of the
transmit antenna support frame assure accurate and
repeatable positioning of the transmit antenna. Both Tx
and Rx antennas are mounted on custom support stands
made of low dielectric, non-conductive plastic material.
Typically, the transmit antenna was WR-284 (2.6 – 3.95
GHz) open ended waveguide, while the receive antenna
was a dual ridged waveguide horn (2 – 18 GHz).
When an experiment is underway, a computer-controlled
linear positioner takes the RX probe through the test zone
in a precise and repeatable manner. It also issues triggers
to a vector network analyzer (VNA) to record field
measurements. The VNA is used to measure a standard
transfer function (s21) between the transmit and receive
antennas, and provide the RF signal to the transmit
antenna. Absolute values of field strength are not
required, since we are comparing differences in the
magnitude and phase of the transmitted field distribution
across a predefined region. Low loss cable was used for
all RF connections to minimize loss and maximize system
dynamic range. The PoP test bed is operated outdoors,
far from other structures.
Anechoic material was
dispersed on the ground between Tx and Rx antennas to
suppress the ground bounce.
3.3 Data Collection and Post-Processing Software Custom software automatically controlled the linear
positioner and VNA, retrieved data from the VNA, and
stored the data in a database. Computer control of the
data collection process facilitated the required accurate
and repeatable measurements of the radiated field of a
single transmit antenna from multiple transmit positions
needed to characterize the properties of an actual PWG.
Synthesis Procedure No. 1: Reading from an input file
that contained all run parameters (file names, geometrical
parameters, electrical parameters) the PWG simulation
used a genetic algorithm to optimize the transmit array
magnitudes and phases (Tx weights). Measurements of the
electric field made by the VNA and stored in a database,
are then exported to an ASCII file of xy-pairs (position,
vector field value). The post-processing software next
reads in the field measurements, applies the simulationspecified amplitude and phase weighting for each channel
of the transmit array, and properly combines the field
measurements (add the weighted values from all files
together at like positions). Again, in this case the transmit
array weights (amplitude and phase) are determined a
priori by a PWG simulation, and the resulting planewave
field is formed from the sum of weighted measurements.
Synthesis Procedure No. 2: Measurements of the
electric field are made by the VNA and stored in a
database; the field data is then exported to an ASCII file
of xy-pairs. The second field synthesis program reads run
parameters from an input file, reads in the values of the
field measurements, and executes the PWG simulation
software to optimize the amplitude and phase weighting
needed to generate the best fit to the desired planewave.
Once the weights are determined a posteriori, it forms the
synthesized field in the same manner described earlier.
4. EXPERIMENTAL RESULTS
This section gives an overview of the results of the
experiment. These results include the measured fields of
a single radiator, of a uniformly excited transmit array,
and of the transmit array weighted to optimize the
planewave properties over the specified region. In
addition, results are presented that illustrate how the PWG
can be used to simulate planewaves arriving from
directions other than normal to the test zone (angle of
arrival, or AoA simulation). Next, data is presented that
illustrates the bandwidth characteristics of the PWG.
Several comparisons of the measured PWG characteristics
with simulations are then presented, and finally data is
shown that indicates scaling properties of the PWG
architecture.
4.1 Nominal PWG Hardware Configuration – The
initial hardware configuration for the experiment
consisted of: 11 transmit locations, each using open-ended
waveguide as a transmit antenna, operation at a frequency
= 3 GHz, a separation between transmit locations =
0.9
0.8
0.7
-1.0
Desired Planewave Region
-0.5
0.0
z - meters
0.5
1.0
1.0
100
0.8
0
-100
0.6
0.4
0.2
-200
Desired Planewave Region
-300
-1.0
-0.5
0.0
z - meters
Desired Planewave Region
0.0
0.5
1.0
-1.0
-0.5
0.0
z - meters
0.5
1.0
Figure 3. Field of a single PWG radiator: (a)
magnitude; (b) phase; and (c) T-factor.
4.3 Field of a Uniformly Excited Array – The transmit
antenna was subsequently positioned at the other eleven
positions that together constitute the virtual PWG. The
radiated field was measured for each transmit antenna
location, and the fields were combine with equal
weighting factors for uniform array excitation. The
resulting amplitude and phase of the field created by the
PWG for uniform weighting is shown in Figure 4. The Tfactor was found to be greater than 0.59 over the region
defined as the desired planewave zone.
4.4 PWG Performance – Next, the eleven field
measurements were combined using weighting factors
determined by the PWG optimization technique described
in [1]. The angle of arrival was specified as 0°. Shown in
Figure 5 are the measured / synthesized values of the field
amplitude (a) and phase (b) over the scanned area that
included the desired planewave region. The T-factor over
the desired planewave region was found to be greater than
0.916. These results demonstrate that the PWG can
produce a field that has significantly better planewave-like
properties than either a single transmit element, or a
field magnitude
1.2
0.8
T > 0.59
0.4
Planewave Region
0.0
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
0.4
0.6
0.8
1.0
phase - degrees
z - meters
40
20
0
T > 0.59
-20
Planewave Region
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
z - meters
Figure 4. Field of PWG for uniform excitation.
field amplitude
1.0
T-factor
Phase - degrees
field magnitude
4.2 Field of One Radiator – The field of a single radiator
was measured across a region that included the desired
planewave zone. Shown in Figure 3 is the measured field
of the middle element of the PWG array. Though the
magnitude (a) of the radiated field is somewhat acceptable
over the desired planewave region due to the broad
beamwidth of the transmit antenna, the phase (b) is seen
to deviate significantly from a planewave condition. The
T-factor [1], shown in (c), varies between 0 and 1. This
also indicates a poor planewave character for the field of
the antenna. The specified / desired planewave region is
indicated by the shading in the graphs.
uniformly excited transmit array of the same size and
configuration as the PWG.
Perfect Amplitude
1.2
1.0
0.8
Defined Planewave Region
0.6
Measured Amplitude
0.4
0.2
-10
-8
-6
-4
-2
0
T > 0.916
2
4
6
8
10
z/l
field phase
0.1016 m (= 1.016 λ = 4.0 inches), a separation between
transmit array and planewave region = 2.5 meters, and a
specified planewave region size = 1 meter in width (10 λ).
The receive antenna (in the planewave region) was a dualridged waveguide horn (AEL-1498). The field was
sampled at 201 points (scanned +/- 30 inches from center
position), or every 0.3 inches. For reference the farfield
of a single transmit radiator = 0.131 meters, while the
farfield of the entire transmit array = 20.64 meters.
Therefore, the planewave region is in the farfield of a
single radiator, but the near field of the entire PWG
transmit array.
Perfect Phase
50
0
-50
Defined Planewave Region
-100
Measured Phase
-150
-10
-8
-6
-4
-2
0
T > 0.916
2
4
6
8
10
z/l
Figure 5. Field of the PWG for optimized excitation.
4.5 Angle of Arrival Simulation – One of the more
interesting possible capabilities of the PWG is its apparent
ability to create fields that mimic the field of planewaves
incident from angles other than the normal. Consider
Figure 6 where the relationship between the angle of
arrival (AoA) and the phase taper over a 1-D region is
shown.
phase - degrees
400
Angle of Arrival = 10 deg
200
Angle of Arrival = 7.5 deg
0
Angle of Arrival = 5 deg
-200
Planewave Region
-400
-0.75
-0.50
-0.25
0.00
0.25
0.50
0.75
z - meters
Figure 7. PWG AoA simulation: AoA = 5; 7.5; and 10°°.
To illustrate the difference, consider that the phase taper
over a 10λ region for a planewave with an AoA = 10° is
Φ=
2π
2π
h sin(φ) = 10λ sin(10) = 10.91 Rad = 625o .
λ
λ
For even moderately sized planewave regions, a relatively
modest value for the angle of arrival can result in a very
large phase taper over a region occupied by an aperture of
interest. Using the same nominal hardware configuration
described earlier, various AoA values were input to the
PWG optimizer. The resulting excitation weights were
then applied to the measured field values, and the PWG
field was synthesized. The phase distribution over the
scanned region for AoA = 5°, 7.5° and 10° are shown in
Figure 7, the minimum values of T-factor for each case
are T > 0.844, 0.748, and 0.632, respectively. As one
would expect, the value of T-factor decreases as the value
of apparent AoA increases.
4.6 PWG Bandwidth – For the PWG to have practical
application in most testing scenarios it must exhibit a
certain bandwidth. In other words, the PWG must
provide planewave-like performance at frequencies about
the center frequency (the frequency at which the
optimized planewave solution has been determined). The
field in the planewave region of the PWG was measured
at frequencies 2.5 – 3.5 GHz for the physical
configuration parameters described earlier.
The
optimized weights were determined for 3.0 GHz (AoA =
0°), then applied to the measured values at all frequencies,
and the resulting PWG synthesized field was formed. The
minimum values of T-factor were then computed over the
specified planewave region, these values are shown in the
graph of Figure 8. The graph shows an excellent solution
at 3 GHz (T > 0.9), but one that declines quickly as the
frequency moves away from the center frequency (T ~ 0.7
for 2.7 – 3.3 GHz). The second curve in the graph is the
planewave fidelity of the solution reached by recomputing
optimized array weights. This result exhibits a much
greater bandwidth
with T > 0.9 over the entire measurement range.
Degradation in T-factor for cases where 3-GHz weights
are applied at other frequencies might have more to do
with the transmit and receive horn properties (variations
in pattern and input impedance with frequency) than with
PWG limitations. This remains an issue under study.
1.0
Minimum T-factor
Figure 6. Geometry for angle of arrival.
0.9
0.8
0.7
Meas. data w/ GA optimized weights
Meas. data w/ 3 GHz weights
0.6
0.5
2.4
2.6
2.8
3.0
3.2
3.4
3.6
frequency - GHz
Figure 8. Bandwidth of PWG solution.
4.7
Comparisons with PWG Simulations – Of
considerable interest is the agreement among measured
values of PWG performance and simulated values.
Shown in Figure 9 are minimum values of the measured
T-factor over the desired test zone as a function of the
simulated angle of arrival (for the baseline PWG
configuration). Also shown in the graph are the values
determined from simulation. One can note excellent
agreement among the measured and simulated values.
Furthermore, the graph shows that for a desired
planewave region of 1.0 m (10λ at 3.0 GHz) the PWG can
generate fields that mimic angles of arrival of 7.5° with T
> 0.8 (phase error < 20°).
4.8 Scaling Characteristics of PWG Architecture –
All results shown to this point have been for the case of
11 transmitters, with a fixed configuration (spacing
separation, etc.), and for a fixed planewave region size
(10λ). For design purposes it is important to know how
the performance of the PWG scales with the number of
transmitters. Shown in Figure 10 are minimum values of
the simulated T-factor over a 10λ-wide test zone as a
function of the simulated angle of arrival, for a 25transmitter PWG configuration. The graph shows that the
PWG can generate fields that mimic angles of arrival to
20.0° with T > 0.8.
1.0
T-factor
0.8
Measurements
Simulations
0.6
show that reasonable PWG configurations demonstrate an
ability to exceed the planewave properties of conventional
radiators (standard gain horn, electrically small antennas,
uniformly excited Tx arrays, etc.).
0.4
1.5
0.2
0.0
0
5
10
15
20
angle of arrival - degrees
Figure 9. Angle of Arrival for PWG configuration: 11
elements.
Test Zone Width (m)
f = 3 GHz
element11 Feb. 25, 2002 2:39:38 PM
Test Zone Range = 2.5 meters
1.0
Tx separation = 4 inches
0.5
tzWidth Feb. 26, 2002 9:03:27 AM
1.0
0.0
3
T-factor
7
9
11
13
15
Number of Radiators
0.8
Figure 12. Planewave region size vs. number of PWG
transmitters.
0.6
0.4
0.2
element25 Feb. 25, 2002 2:40:54 PM
0.0
0
5
10
15
20
25
30
angle of arrival - degrees
Figure 10. Angle of Arrival for PWG configuration:
25 elements.
Next shown in Figure 11 are the minimum values of
measured T-factor over the planewave region as a function
of planewave region size (number of PWG transmitters =
11). The graph shows that T > 0.8 for planewave region
sizes to 15λ are possible for a PWG with 11 transmitters
(AoA = 0°). Also shown in the graph are the minimum
values determined by simulation. Excellent agreement is
again noted among measured and simulated values.
Finally, the PWG test bed was used to determine how the
PWG capability scales with the size (number of
transmitters) of the PWG. Shown in Figure 12 is the
experimentally determined maximum test zone width with
a T > 0.9 as a function of the number of transmitters in the
PWG array. The data shows a planewave size scaling
factor of approximately 1λ / transmitter for the equally
spaced arrays considered here.
1.0
field minimum T-factor
5
Simulation
Measurement
0.8
0.6
N = 11
Tx separation = 4-inches
Planewave region range = 2.5-m
frequency = 3 GHz
0.4
0.2
TZsizeCOMP Feb. 23, 2002 12:12:33 PM
0.0
0
2
4
6
8
10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
planewave region size / l
Figure 11. T-factor vs. size of planewave region.
5. SUMMARY
The purpose of the work reported in this paper was to
experimentally demonstrate the concepts and operation of
a Planewave Generator. First, the experimental results
We have shown that the PWG demonstrates an
exceptional capability to create flat amplitude tapers over
a specified and spatially limited planewave region, and an
extraordinary capability to create phase tapers that mimic
planewaves with arbitrary angles of arrival. Also, we
have illustrated that PWG simulation fields and PWG
measurements are in good / excellent agreement, and that
the size of the planewave region and AoA simulation
capability scales with the number of radiators in the Tx
array. Both simulation and measurements show sufficient
practical bandwidth. Much further work remains in the
design of hardware and software, and validation of a
prototype PWG.
6. REFERENCES
[1] C. Courtney, D. Voss, R. Haupt and L. LeDuc, “The
Theory and Architecture of a Planewave Generator,”
AMTA 2002, Cleveland, 2002.
[2] Electromagnetic Waves and Radiating Systems, E. C.
Jordan and K. G. Balmain, 2nd edition, Prentice Hall
Inc., Englewood Cliffs, NJ, 1968.
7. ACKNOWLEDGMENTS
This work was supported in part by the United States Air
Force under the Small Business (SBIR) Innovation
Research program. The authors wish to thank the
following individuals for their contributions to the
development of this technology:
Mr. Abraham
Atachbarian (EAFB SBIR Program Manager), Ms. Joanne
Eldredge (EAFB Contracting Office), Mr. Mark Timmons
and Mr. Ged Bluzas (EAFB, former Project Officers), Mr.
Dave Slemp (Agilent Technologies), and Dr. Bill Swartz,
Mr. Frank Elwood, Mr. Mike Thomas and Mr. Philip
Critelli (Voss Scientific).